. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. E VOLUTE. all the centres ofthe that ofculate ilie curve AM, rib i! b) e\ Jution. 2. \ I of curvature, or radius of 1 C, is equal to the arc DC; or to tl - the clement of the arc M curve defcribed by evol is an arc < ibed by the radius C M ; the radius of the evolut • pec- A M, or to a tangent at M. 4. Since the radius of the crolute MC is tangent to the evolute BCF| curves by evolution be defcribed through innumerable , if only tangents be produced in the 1 I points
. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. E VOLUTE. all the centres ofthe that ofculate ilie curve AM, rib i! b) e\ Jution. 2. \ I of curvature, or radius of 1 C, is equal to the arc DC; or to tl - the clement of the arc M curve defcribed by evol is an arc < ibed by the radius C M ; the radius of the evolut • pec- A M, or to a tangent at M. 4. Since the radius of the crolute MC is tangent to the evolute BCF| curves by evolution be defcribed through innumerable , if only tangents be produced in the 1 I points of the e volute, till they become equal to their correfpondent arcs. The finding of the radii of evolutes is a thing of great importance in the higher fpeculations of geometry ; and even, Gotnetiroes, is of ufe in practice as the inventor being equal to = —, we (hall have, by fubititut- ° ' 4 a >: 4 a- ing theie values in the expreffion for y and y,. defcribed through the point B, C n be bifefted in H, and H r be made equal 2 A C, and r E be a perpendi- cular at r, produced till it meets a line B E, drawn from B through H, this line B E will be the radius of cur- vature required: for BC =ACxCa, 35 E. 3. or — = C«| n = C n, and C H = ~ a, and AC * " C r = i a + 2 x ; and by 47 E. I. C H" + C IF 5 =B H, i. t. % a" + a x; a : Cr B H ; and by 4 E. 6. C H : H B :: a + 4 x a BE; i. e. ia: J «* + «*)! :: ±a + 2 x : " + 4 '" X Ja1 a' — 4a .vi 1 ; Ta1 yj — B E as before. A D the vertical diftance, or, —, is in this cafe, putting — for j, x 2y and 1 for x, equal to - ; and this likewife appears, by con- fidering, that in the expreffion for the radius when die radius becomes equal to the vertical dutance, the abfeifs x vaniihes, and it becomes a' a 2 a- 2 d: 2 2. To find the radius of curvature at any point B in the cycloid A B D,_/ff. 5. Put the radius O F or 0 D = a, abfeifs AC = », ordi- nate. Please note that these im
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Keywords: ., bookcentury1800, bookdecade1810, booksubjectencyclo, bookyear1819
